[01] Scott Nakatani, Space Systems Academic Group, Naval Postgraduate School, Monterey, USA. [02] Timothy Sands, Mechanical Engineering, Stanford University, Stanford, USA.

The nature of adaptive controls, or controls for unpredictable systems, lends itself naturally to the concept of damage tolerant controls in high performing systems, such as aircraft and spacecraft. Recent technical demonstrations of damage tolerant aircraft prove the concept of adaptive controls in an operational environment. Research covered by this paper expands on the topic by discussing the application of adaptive controls to spacecraft and theory behind simulating damage tolerant control implementation. Simulation is then used to demonstrate the stability of adaptive controls when experiencing sudden mass loss and rapid changes in inertia.

On-Orbit Damage, Autonomous Systems, Nonlinear Controls, Adaptive Controls, Luenberger, Modified Pid Control

[01] P. Baines, “Prospects for non-offensive defenses in space,” Center for Nonproliferation Studies Occasional Paper, no. 12, pp 31-48. Aug, 2003. [02] United State Strategic Command, “USSTRATCOM space control and space surveillance factsheet,” USSTRATCOM, Offutt AFB, NE, Dec. 2012. [03] D. Kessler and B. Cour-Palais, “Collision frequency of artificial satellites: The creation of a debris belt,” Journal of Geophysical Research, vol. 83, no. A6, pp 2637-2646, Jun. 1978. [04] “Satellite collision leaves significant debris cloud,” Nat. Aeronautics and Space Admin. Orbital Debris Quarterly News, vol. 13, no. 2, pp. 1-2, Apr. 2009. [05] “International Space Station again dodges debris,” Nat. Aeronautics and Space Admin. Orbital Debris Quarterly News, vol. 15, no. 3, pp. 1-2, Jul. 2011. [06] S. Kan, “China’s anti-satellite weapon test,” U.S. Library of Congr., Congressional Research Service, Washington, D. C., Rep. RS22652, Apr. 2007. [07] T. Kelso. (2013, March 8). Chinese space debris may have hit Russian satellite [Online]. Available: http://www.blogs.agi.com/agi/2013/03/08/chinese-space-debris-hits- russian-satellite/ [08] Rockwell Collins. (2011). Case study: Rockwell Collins demonstrates damage tolerant flight controls and autonomous landing capabilities [Online]. Available: http://www.rockwellcollins.com/sitecore/content/Data/Success_Stories/DARPA_Damage_Tolerance.aspx [09] Rockwell Collins. (2011, August 18). DARPA, U. S. Army and Rockwell Collins release video of successful damage tolerance control testing on shadow unmanned aircraft system. [Online]. Available: http://www.rockwellcollins.com/sitecore/content/Data/News/2011_Cal_Yr/GS/FY11GSNR32-DTC_Shadow.aspx [10] J.-J. Slotine and W. Li, “Nonlinear control systems design” in Applied nonlinear control, Upper Saddle River: Prentice Hall, 1991, ch. 6-9, pp 191-432. [11] K. Åström and B. Wittenmark, “What is adaptive control?” in Adaptive Control, 2nd ed. Mineola: Dover Publications, 2008, pp. 376. [12] G. Dumont and M. Huzmezan, “Concepts, methods and techniques in adaptive control,” in Proceedings of the American Control Conference, Vancouver, B. C., 2002, pp. 1137-1150. [13] N. Hovakimyan, “Robust adaptive control of multivariable nonlinear systems,” Univ. of Illinois, Urbana, IL, Rep. AFRL-OSR-VA-TR-2012–0524, 2011. [14] J. Peters and S. Schaal, “Reinforcement learning by reward-weighted regression for operational space control,” in Proceedings of the 24th International Conference on Machine Learning, Tuebingen, Germany, 2007, pp. 745-750. [15] E. Liebemann et al., “Light commercial vehicles: challenges for vehicle stability control,” Robert Bosch GmbH, Gerlingen, Germany, Rep. 07-0269, 2007. [16] Man Truck & Bus. (2012). Adaptive cruise control. Available [Online] at the following weblink/URL: http://www.mantruckandbus.com/com/en/innovation___competence/applied_safety/adaptive_cruise_control__acc_/Adaptive_Cruise_Control__ACC_.html [17] W. Pananurak et al., “Adaptive cruise control for an intelligent vehicle,” in Proceedings of the 2008 IEEE International Conference on Robotics and Biometrics, Bangkok, Thailand, 2008, pp. 1794-1799. [18] W. MacKunis et al., “Adaptive satellite attitude control in the presence of inertia and CMG gimbal friction uncertainties,” The Journal of the Astronautical Sciences, vol. 56, no. 1, pp. 121-134, Jan. 2008. [19] A. Tewari, “Adaptive vectored thrust deorbiting of space debris,” Journal of Spacecraft and Rockets, vol. 50, no. 2, pp. 394-401, Mar. 2013. [20] Staff of the Flight Research Center, “Experience with the X-15 adaptive flight control system,” NASA, Edwards, CA, Rep. NASA TN H-618, 1971. [21] S. Lilley, “Vicious cycle,” In National Aeronautics and Space Administration System Failure Case Studies, vol. 5, no. 3, pp. 1-4, 2011. [22] A. Ulsoy and Y. Koren, “Applications of adaptive control to machine tool process control,” in IEEE Control Systems Magazine, vol. 9, no. 4, pp. 33-37, Jun. 1989. [23] A. Taylor, “Adaptive attitude control for long-life space vehicles,” General Electric Company, Binghampton, NY, Rep. AIAA Paper No. 69–945, 1969. [24] C.-H. Ih et al., “Application of adaptive control to space stations,” Jet Propulsion Laboratory, Pasadena, CA, Rep. AIAA Paper 85-1970, 1985. [25] B. Govin et al., “Adaptive control of flexible space structures,” in American Institute of Aeronautics and Astronautics Guidance and Control Conference, Velizy, France, pp. 192-199, 1981. [26] R. Kosut, “Adaptive control techniques for large space structures,” Integrated Systems Inc., Bolling AFB, Washington D.C., Rep. AFOSR-TR-89–0071, 1989. [27] D. Schaechter, “Adaptive control for large space structures,” in Aeronautics and Astronautics Guidance and Control Conference, Palo Alto, CA, pp. 606-611, 1983. [28] Y. Xu et al., “Adaptive control of space robot system with an attitude controlled base,” Carnegie Mellon University, Pittsburgh, PA, Rep. CMU-RI-TR-91-14, 1991. [29] H. Ho, et al., “Comparative studies of three adaptive controllers,” in ISA Transactions, vol. 38, no. 1, pp. 43-53, Jan. 1999. [30] L. Ehrenwald and M. Guelman, “Integrated adaptive control of space manipulators,” in Journal of Guidance, Control, and Dynamics, vol. 21, no. 1, pp. 156-163, Jan. 1998. [31] B. Wie, “Rotational maneuvers and attitude control,” in Space Vehicle Dynamics and Control, 2nd ed., Reston, VA, Amer. Inst. of Aeronautics and Astronautics Inc., 2008, ch. 7, pp. 423-466. [32] E. Reeves, “Spacecraft design and sizing,” in Space Mission Analysis and Design, 3rd ed., Hawthorne, CA, Microcosm Press, 1999, pp. 324-325. [33] Mathworks. (2013). Quaternion to direction cosine matrix r2013a, [Online] Available: http://www.mathworks.com/help/aeroblks/quaternionstodirectioncosinematrix.html [34] B. Wie, “Rigid Body Dynamics,” in Space Vehicle Dynamics and Control, 2nd ed., Reston, VA, Amer. Inst. of Aeronautics and Astronautics Inc., 2008, ch. 6, pp. 328-335. [35] D. Hoag, “Apollo guidance and navigation considerations of Apollo IMO gimbal lock,” Massachusetts Institute of Technology, Cambridge, MA, Rep. E-1344, 1963. [36] D. Luenberger, Introduction to dynamic systems: theory, models, and applications, New York City, NY, John Wiley & Sons, 1979, pp. 300-307. [37] G. Welch and G. Bishop, An introduction to the Kalman filter, Chapel Hill, NC, University of North Carolina, 2006, pp. 2-15. [38] B. Wie, “Dynamic Systems Control,” in Space Vehicle Dynamics and Control, 2nd ed., Reston, VA, Amer. Inst. of Aeronautics and Astronautics Inc., 2008, ch. 2, pp. 137. [39] N. Metropolis, “The beginning of the Monte Carlo method,” in Los Alamos Science, Special Issue, 1987, pp. 125-130. [40] J. Wertz and W. Lason, “Applying the space mission analysis and design process,” in Space Mission Analysis and Design, 3rd ed., Hawthorne, CA, Microcosm Press, 1999, pp. 301. [41] T. Sands, "Physics-Based Control Methods," book chapter in Advancements in Spacecraft Systems and Orbit Determination, In-Tech Publishers, pp. 29-54, 2012. [42] T. Sands, Improved Magnetic Levitation via Online Disturbance Decoupling", Physics Journal, 1(3) 272-280, Oct. 2015. [43] T. Sands, J. Kim, B. Agrawal, "Experiments in Control of Rotational Mechanics", International Journal of Automation, Control and Intelligent Systems, 2(1) 9-22, Jan. 2016.